The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Mathematical Logic Quarterly 42 (1):410-420 (1996)
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Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2math image and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second



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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
General Topology.John L. Kelley - 1962 - Journal of Symbolic Logic 27 (2):235-235.
The Axiom of Choice.Gershon Sageev - 1976 - Journal of Symbolic Logic 41 (4):784-785.

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